Question

State if the following statements are true and which are false? Justify your answer with a
short proof or a counterexample

If W1 and W2 are subspaces of vector space V and W1+W2 =V, thenW1∩W2 = {0}

Answer 1

Answer on Question #44919 – Math - Linear Algebra

If $W_{1}$ and $W_{2}$ are subspaces of vector space $V$ and $W_{1} + W_{2} = V$, then $W_{1} \cap W_{2} = \{0\}$

Answer

False. $W_{1} \cap W_{2} = \{0\}$ for subspaces $W_{1}$ and $W_{2}$ of vector space $V$ means that $W_{1} \oplus W_{2} = V$, but direct sum is only the special case of $W_{1} + W_{2}$.

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